Pre-Algebra Examples

Add: $\frac{5 y}{x} + \frac{3 x}{y}$

Step 1

To write $\frac{5 y}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{5 y}{x} \cdot \frac{y}{y} + \frac{3 x}{y}$

Step 2

To write $\frac{3 x}{y}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5 y}{x} \cdot \frac{y}{y} + \frac{3 x}{y} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x y$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 y}{x}$ by $\frac{y}{y}$ .

$\frac{5 y \cdot y}{x y} + \frac{3 x}{y} \cdot \frac{x}{x}$

Step 3.2

Multiply $\frac{3 x}{y}$ by $\frac{x}{x}$ .

$\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{y x}$

Step 3.3

Reorder the factors of $y x$ .

$\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 y \cdot y + 3 x \cdot x}{x y}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $y$ by $y$ by adding the exponents.

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Step 5.1.1

Move $y$ .

$\frac{5 (y \cdot y) + 3 x \cdot x}{x y}$

Step 5.1.2

Multiply $y$ by $y$ .

$\frac{5 y^{2} + 3 x \cdot x}{x y}$

Step 5.2

Multiply $x$ by $x$ by adding the exponents.

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Step 5.2.1

Move $x$ .

$\frac{5 y^{2} + 3 (x \cdot x)}{x y}$

Step 5.2.2

Multiply $x$ by $x$ .

$\frac{5 y^{2} + 3 x^{2}}{x y}$